Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 200 of C. The current share prices are $42.67, $81.33, and $58.22, respectively. The expected returns and the covariances are provided in the table below. Expected Return Covariance Stock A 12.00% Stock B Stock C 9.40% 14.00% Assume the risk-free rate is 5%. Stock A 0.09164319 -0.0188809 -0.0022386 Stock B -0.01888085 0.03885393 -0.0005562 Stock C -0.00223864 -0.0005562 0.0080718 1. Compute the Sharpe ratio of your current portfolio. 2. You want to trade stocks so that you can maximize the Sharpe ratio of your portfolio. There is a 1% fee on selling or trading each stock. For example, if you sell 10 shares of Stock A and buy 5 shares of Stock B, the total dollar amount traded is 10*$42.67+5*$81.33=$833.35 and you have to pay a transaction fee of $8.33. These two transactions generate a net amount of 10*$42.67 - 5*$81.33 - $8.34 =$11.71 in cash. You would like this net amount to be always non-negative but no more than $5. Also, you cannot have short position in any stock, i.e., you cannot sell more than what you have. 1 Formulate a nonlinear optimization model that determines the number of shares of each stock to buy and sell. For simplicity, the solution for this problem is not required to be integers.